Muse didn’t set out to make the most gloriously ambitious album of their career. How could they have? The band who dreamt up Supermassive Black Hole, Knights Of Cydonia, and the three-part Exogenesis symphony were already well-versed in going one louder. Any wilder, any further out there, and Muse would risk incineration by a dwarf star of their own making.

But you don’t become one of the biggest bands on this planet — selling 15 million albumsworldwide, five MTV Europe Awards, two Brit Awards, eight NME Awards, five Q Awards, four Kerrang! Awards, and winner of the 2011Best Rock Album Grammy; No 1 in 19 countries with 2009’s The Resistance; filler of arena and stadiums across the world — by sitting on your hands.

So when Muse approached the making of their sixth studio album, The 2nd Law, they wouldn’t skimp on the choirs, strings, and horn sections. And rest assured: guitar-shredding, piano-thumping, orchestra-arranging, book-chewing, big-thinking Matt Bellamy, as the band’s chief songwriter, didn’t lower his sights from The Big Picture nor ignore The Precious Details. Nor were the trio afraid of giving space to a brilliant new element to their sound — songs written and sung by bass player Chris Wolstenholme.

What the Devon-born band of school friends did do different was this: they made things easy for themselves. For the first time since the dawn of their career in small town England 18 years ago, all three members were living in the same place during the making of an album. Domiciled in and around London, they booked a recording studio, Air, and came and went as they pleased.

“We all had great fun doing it,” says Wolstenholme, “and hopefully you can hear that on the album. There are some real moments of positivity in the songs. And I just think everyone personally is in a pretty good place at the moment.” Adds drummer Dom Howard, “It feels like the best thing we’ve ever done. There was a sense of adventure making it.”

“This was a breeze!” declares Bellamy, still high from the experience of seeing rock-operatic new track Survival emerge victorious as the official anthem for the London 2012 Olympics. “We were making ourselves laugh at times with how different things were sounding.”

As Howard accurately describes it, The 2nd Law brims with “wild” sounds. It’s exactly what Muse had in mind when they sat down last October after the completion of the two-year Resistance world tour. Within four quick weeks the trio had 13 tracks in embryonic but viable form.

From solid beginnings came big tunes. Madness, the album’s naggingly infectious first single, pulses with a grimy throb. It sounds nothing like Muse, and it sounds everything like Muse. “I wanted to do something really minimal,” Bellamy says. “Essentially it’s 12-bar blues. I think it’s probably the best song I’ve ever written. And one of the most personal songs I’ve written. It’s kind of about that time when you’re with your girlfriend and that moment where you have a fight and she walks out the house and leaves you on your own to think about it. And you’re going, ‘No way! She was right! Of course she was right!’”

Album opener Supremacy was one of the first songs Muse worked on. Bellamy’s early sketch grabbed Wolstenholme immediately, “because it was just so all over the place,” he says. “It starts off and you think it’s this dirty, grungy metal… thing. Then by the time you get to the verse it’s gone into pure film music. I said to Matt at the time that it reminded me of Wings.”

“We were layering up loads and loads of snare drums,” adds Howard. “There were tons of tympani and bass drums and weird percussion. The idea is it should sound like a marching band coming over the hill, just behind the orchestra. Then it goes off into some Live And Let Die-style freak-out section in the middle. It felt like something different. We really wanted it to sound like a big, live, massive stadium rock track. We were thinking that way when we recorded it — we had a big PA set up, and the room was shaking to this massive drum sound. Then the verse goes on this completely different journey from the riff — it’s a little wink back to that Ennio Morricone influence which you hear on Knights Of Cydonia.”

Soundtracks, affirms Bellamy, have long been an under-heralded influence on his writing. On The 2nd Law, this enthusiasm dovetails with his love of classical music. On previous Muse albums, his orchestral excursions have been influenced by Rachmaninoff and Berlioz. This time the inspirations were contemporary composers and Hollywood legends such as Hans Zimmer and John Williams.

As ever with Matt Bellamy, when it came to writing the lyrics, there were themes big and small he wanted to address. The sinuous funk of Animals began with a jam and now, in its recorded version, ends with a sample of bellowing Wall Street stockbrokers. “That’s the song aimed at the Fred Goodwins of this world,” says Bellamy of the disgraced British banker. “It’s looking at people who are instrumental in bringing down whole countries.”

The lyrics and ideas behind Explorers, like those of the two-part title track, tap into the album’s more philosophical side — Bellamy’s thoughts on the depletion of the planet’s energies and resources. But he also applies this thermodynamic theory to the ebb and flow of passion in relationships, as heard in Big Freeze and Madness.

But as Wolstenholme underlines, The 2nd Law is far from a sombre album. “There are some negative undertones, sure. But it’s all about human responses to them and the things we do to get through life. That’s a positive thing.”

In any case, any album that includes both Survival, their po(m)p and circumstance Olympic anthem, and a song with the Queen-go-disco abandon of Panic Station can’t, ultimately, take itself too seriously. “We weren’t afraid of doing something that’s just a dancing track,” says Bellamy of the latter song, a groovy belter recorded with a horn section comprising classic Chicago players (one of whom played on Stevie Wonder’s Superstition).

“There’s an eccentricity to the album which makes it fun,” Bellamy says. “I don’t think it’s taking itself too seriously even though some of the lyrics are.

I’d go so far as to say we had a bit of a laugh making this album. The spirits were up, more so than on any previous Muse album, that’s for sure.”